What are the divisors of 3516?

1, 2, 3, 4, 6, 12, 293, 586, 879, 1172, 1758, 3516

There is a total of 12 positive divisors.
The sum of these divisors is 8232.
The arithmetic mean is 686.

8 even divisors

2, 4, 6, 12, 586, 1172, 1758, 3516

4 odd divisors

1, 3, 293, 879

How to compute the divisors of 3516?

A number N is said to be divisible by a number M (with M non-zero) if, when we divide N by M, the remainder of the division is zero.

$N mod M = 0$

Brute force algorithm

We could start by using a brute-force method which would involve dividing 3516 by each of the numbers from 1 to 3516 to determine which ones have a remainder equal to 0.

$Remainder = N - (M \times ⌊ \frac{N}{M} ⌋)$

(where $⌊ \frac{N}{M} ⌋$ is the integer part of the quotient)

3516 / 1 = 3516 (the remainder is 0, so 1 is a divisor of 3516)
3516 / 2 = 1758 (the remainder is 0, so 2 is a divisor of 3516)
3516 / 3 = 1172 (the remainder is 0, so 3 is a divisor of 3516)
...
3516 / 3515 = 1.0002844950213 (the remainder is 1, so 3515 is not a divisor of 3516)
3516 / 3516 = 1 (the remainder is 0, so 3516 is a divisor of 3516)

Improved algorithm using square-root

However, there is another slightly better approach that reduces the number of iterations by testing only integers less than or equal to the square root of 3516 (i.e. 59.295868321494). Indeed, if a number N has a divisor D greater than its square root, then there is necessarily a smaller divisor d such that:

$D \times d = N$

(thus, if $\frac{N}{D} = d$ , then $\frac{N}{d} = D$ )

3516 / 1 = 3516 (the remainder is 0, so 1 and 3516 are divisors of 3516)
3516 / 2 = 1758 (the remainder is 0, so 2 and 1758 are divisors of 3516)
3516 / 3 = 1172 (the remainder is 0, so 3 and 1172 are divisors of 3516)
...
3516 / 58 = 60.620689655172 (the remainder is 36, so 58 is not a divisor of 3516)
3516 / 59 = 59.593220338983 (the remainder is 35, so 59 is not a divisor of 3516)